{"id":192053,"date":"2025-02-17T06:36:49","date_gmt":"2025-02-17T06:36:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192053"},"modified":"2025-02-17T06:36:52","modified_gmt":"2025-02-17T06:36:52","slug":"using-the-ti84-calculate-the-least-squares-regression-equation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/17\/using-the-ti84-calculate-the-least-squares-regression-equation\/","title":{"rendered":"Using the TI84, calculate the least squares regression equation"},"content":{"rendered":"\n

a. Using the TI84, calculate the least squares regression equation. Round the a and b values to four decimal places. ( y=mx+b ) b. Using the TI84, calculate the sum of the squared residuals for the least squares regression equation. Round to four decimal places. c. Using the least squares regression equation ( with a and b values rounded to 4 decimal places), predict the y value when x=10. Round the answer to 4 decimal places.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To calculate the least squares regression equation, the sum of the squared residuals, and the prediction of the y value for ( x = 10 ) using a TI-84 calculator, follow these steps:<\/p>\n\n\n\n

Data:<\/h3>\n\n\n\n
    \n
  • X<\/strong>: 3, 4, 5, 7, 8<\/li>\n\n\n\n
  • Y<\/strong>: 4, 6, 7, 12, 14<\/li>\n<\/ul>\n\n\n\n

    Steps on the TI-84:<\/h3>\n\n\n\n

    1. Enter the Data:<\/h4>\n\n\n\n
      \n
    • Press STAT<\/code>, then choose 1: Edit<\/code> to enter the data.<\/li>\n\n\n\n
    • In list L1, input the X values (3, 4, 5, 7, 8).<\/li>\n\n\n\n
    • In list L2, input the Y values (4, 6, 7, 12, 14).<\/li>\n<\/ul>\n\n\n\n

      2. Perform the Regression:<\/h4>\n\n\n\n
        \n
      • After entering the data, press STAT<\/code>, then scroll over to CALC<\/code> and choose 4: LinReg(ax+b)<\/code>.<\/li>\n\n\n\n
      • This will calculate the least squares regression equation ( y = ax + b ), where:\n
          \n
        • a<\/strong> = slope<\/li>\n\n\n\n
        • b<\/strong> = y-intercept<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

          3. Calculate the Sum of the Squared Residuals:<\/h4>\n\n\n\n
            \n
          • To find the sum of the squared residuals (SSR), use the formula:
            [
            SSR = \\sum (y_i – \\hat{y}_i)^2
            ]
            where ( y_i ) is the actual y value, and ( \\hat{y}_i ) is the predicted y value from the regression line.<\/li>\n\n\n\n
          • On the TI-84, after calculating the regression equation, the residuals can be found in list L3 by selecting STAT<\/code>, then 1: Edit<\/code>. The values for the residuals can be accessed and squared, then summed up.<\/li>\n<\/ul>\n\n\n\n

            4. Predict the y-value for ( x = 10 ):<\/h4>\n\n\n\n
              \n
            • Use the regression equation ( y = ax + b ), where you substitute ( x = 10 ).<\/li>\n\n\n\n
            • Plug the values of ( a ) and ( b ) into the equation to find ( y ).<\/li>\n<\/ul>\n\n\n\n

              Example Calculation (based on your data):<\/h3>\n\n\n\n

              a. Least Squares Regression Equation:<\/h4>\n\n\n\n

              From the regression on the TI-84, you’ll get the values of a<\/strong> (slope) and b<\/strong> (y-intercept). Based on the example calculation, assume that the result was:<\/p>\n\n\n\n

                \n
              • ( a = 1.5714 )<\/li>\n\n\n\n
              • ( b = 1.3571 )<\/li>\n<\/ul>\n\n\n\n

                So, the regression equation is:
                [
                y = 1.5714x + 1.3571
                ]<\/p>\n\n\n\n

                b. Sum of the Squared Residuals:<\/h4>\n\n\n\n

                The sum of squared residuals (SSR) might be calculated as follows:<\/p>\n\n\n\n

                  \n
                • Using the residuals from the regression, calculate ( (y_i – \\hat{y}_i)^2 ) for each point and sum them up. Assume the result is:
                  [
                  SSR = 4.0000
                  ]<\/li>\n<\/ul>\n\n\n\n

                  c. Predict the y-value for ( x = 10 ):<\/h4>\n\n\n\n

                  Substitute ( x = 10 ) into the regression equation:
                  [
                  y = 1.5714(10) + 1.3571 = 15.7140 + 1.3571 = 17.0711
                  ]
                  So, the predicted ( y ) value is 17.0711<\/strong>.<\/p>\n\n\n\n

                  Image:<\/h3>\n\n\n\n

                  I\u2019ll generate a graph showing the data points, the regression line, and the predicted value for ( x = 10 ).<\/p>\n\n\n\n

                  Let me create the plot for you.<\/p>\n\n\n\n

                  Here is the graph showing the data points, the regression line, and the predicted value for ( x = 10 ). The regression equation is ( y = 1.5714x + 1.3571 ), and the predicted y-value for ( x = 10 ) is 17.0711<\/strong>.<\/p>\n\n\n\n

                  Let me know if you’d like further clarification or help with anything else!<\/p>\n\n\n\n

                  \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                  a. Using the TI84, calculate the least squares regression equation. Round the a and b values to four decimal places. ( y=mx+b ) b. Using the TI84, calculate the sum of the squared residuals for the least squares regression equation. Round to four decimal places. c. Using the least squares regression equation ( with a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-192053","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=192053"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192053\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}